Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is :

# Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is :

1. A

170

2. B

190

3. C

180

4. D

210

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### Solution:

Since, 20 pillars are connected by beams with all  its non adjacent pillars.

$\therefore$ Total number of beams ${=}^{20}{C}_{2}-20$

$=\frac{20!}{18!2!}-20=\frac{20×19}{2}-20=170$

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